The present disclosure relates to an improved sigma-delta modulator circuit. Sigma-delta modulator circuits are often used for analog-to-digital data conversion, but sigma-delta modulator circuits operating with low input signal values or with only DC inputs may be vulnerable to limit cycles. That is, the output spectrum may include noticeable power in spurious tones that were not present in the input signal. The tones arise because the nonlinear sigma-delta modulator circuit output bits sometimes enter a repeating pattern, resulting in signal-to-noise ratio (SNR) degradation. Commonly-assigned U.S. Pat. No. 8,766,836B2, which describes an example of a sigma delta modulator with dither, is hereby incorporated by reference in its entirety.